Answer
$\dfrac{28}{25}-\dfrac{21}{25}i$
Work Step by Step
Multiplying by the conjugate of the denominator of $
\dfrac{7}{4+3i}
$ results to
\begin{array}{l}
\dfrac{7}{4+3i}
\cdot
\dfrac{4-3i}{4-3i}
\\\\=
\dfrac{28-21i}{(4)^2-(3i)^2}
\\\\=
\dfrac{28-21i}{16-9i^2}
\\\\=
\dfrac{28-21i}{16-9(-1)}
\\\\=
\dfrac{28-21i}{25}
\\\\=
\dfrac{28}{25}-\dfrac{21}{25}i
.\end{array}
